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Understanding the mechanisms behind human mobility patterns is crucial toimprove our ability to optimize and predict traffic flows. Two representativemobility models, i.e., radiation and gravity models, have been extensivelycompared to each other against various empirical data sets, while theirfundamental relation is far from being fully understood. In order to study sucha relation, we first model the heterogeneous population landscape by generatinga fractal geometry of sites and then by assigning to each site a populationindependently drawn from a power-law distribution. Then the radiation model onthis population landscape, which we call the radiation-on-landscape (RoL)model, is compared to the gravity model to derive the distance exponent in thegravity model in terms of the properties of the population landscape, which isconfirmed by the numerical simulations. Consequently, we provide a possibleexplanation for the origin of the distance exponent in terms of the propertiesof the heterogeneous population landscape, enabling us to better understandmobility patterns constrained by the travel distance.

Gravity model explained by the radiation model on a population landscape